These images were originally produced because Arecibo happened to be studying this particular asteroid, which turned out to have a lot of fun attributes for public outreach. You can also find them and a bit more detail on my blog posts here and here.
Asteroid 1998QE2 was given celebrity status by virtue of the fact that it made a close approach to Earth on 31st May 2013 (3.6 million miles, about 15 times the distance to the Moon) and happens to have QE2 in its name. Apparently, that's entirely a coincidence due to the naming convention when discovering asteroids and not actually related to the famous ocean liner in any way. But fortuitously, 1998QE2 is just about the right size (1.7 miles in diameter) for comparisons with its more well-known namesake to be somewhat meaningful. The asteroid is about 9 ship-lengths across :
... which makes it about 29 ship-lengths in circumference...
... and about as massive as 300,000 QE2s.
And it also has its own moon ! One that's only slightly bigger than the space station! That practically hands this to me on a silver platter...
Further analysis showed that not only is 1998QE2 roughly spherical, but that it's of such low density that it would probably float. Its surface gravity is so low you could (if you were very VERY careful) jump off and land on its moon. For these reasons, I pronounce 1998QE2 to be the best space rock ever (not counting 2013BATATAS, obviously).